<h2>题目编号 : 281</h2>
<div style="color:#666;font-size:80%;">05 March 2010</div><br />
<div class="problem_content">
<p>You are given a pizza (perfect circle) that has been cut into <var>m</var>&middot;<var>n</var> equal pieces and you want to have exactly one topping on each slice.</p>

<p>Let <var>f</var>(<var>m</var>,<var>n</var>) denote the number of ways you can have toppings on the pizza with <var>m</var> different toppings (<var>m</var>&thinsp;<img src='images/symbol_ge.gif' width='10' height='12' alt='&ge;' border='0' style='vertical-align:middle;' />&thinsp;2), using each topping on exactly <var>n</var> slices (<var>n</var>&thinsp;<img src='images/symbol_ge.gif' width='10' height='12' alt='&ge;' border='0' style='vertical-align:middle;' />&thinsp;1). <br />Reflections are considered distinct, rotations are not. </p>

<p>Thus, for instance, <var>f</var>(2,1)&thinsp;=&thinsp;1, <var>f</var>(2,2)&thinsp;=&thinsp;<var>f</var>(3,1)&thinsp;=&thinsp;2 and <var>f</var>(3,2)&thinsp;=&thinsp;16. <br /><var>f</var>(3,2) is shown below:</p>

<div align='center'><img src="project/images/p_281_pizza.gif" /></div>

<p>Find the sum of all <var>f</var>(<var>m</var>,<var>n</var>) such that <var>f</var>(<var>m</var>,<var>n</var>)&thinsp;<img src='images/symbol_le.gif' width='10' height='12' alt='&le;' border='0' style='vertical-align:middle;' />&thinsp;10<img src="" style="display:none;" alt="^(" /><sup>15</sup><img src="" style="display:none;" alt=")" />.</p>
</div><br />
